A non-symmetric polymerase chain reaction (PCR) amplification method employing a limiting primer in low concentration whose concentration-adjusted melting point at least equals, and preferably exceeds, that of the excess primer, the latter in turn not being more than 25.degree. C. below the melting temperature of the amplicon. Assays employing such amplification and labeled hybridization probes, including assays that include a detection step following primer extension or a low-temperature probe, or both. Kits for performing such assays and primer or primer-and-probe sets for performing the foregoing amplifications and assays.